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arXiv · 2108.03281

Globally optimizing QAOA circuit depth for constrained optimization problems

Rebekah Herrman·Lorna Treffert·James Ostrowski·Phillip C. Lotshaw·Travis S. Humble·George Siopsis
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Abstract

We develop a global variable substitution method that reduces $n$-variable monomials in combinatorial optimization problems to equivalent instances with monomials in fewer variables. We apply this technique to $3$-SAT and analyze the optimal quantum circuit depth needed to solve the reduced problem using the quantum approximate optimization algorithm. For benchmark $3$-SAT problems, we find that the upper bound of the circuit depth is smaller when the problem is formulated as a product and uses the substitution method to decompose gates than when the problem is written in the linear formulation, which requires no decomposition.

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Rebekah Herrman, Lorna Treffert, James Ostrowski, Phillip C. Lotshaw, Travis S. Humble, George Siopsis. 2021-08-06. Globally optimizing QAOA circuit depth for constrained optimization problems. https://arxiv.org/abs/2108.03281

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